{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T15:13:41Z","timestamp":1772032421024,"version":"3.50.1"},"reference-count":60,"publisher":"Wiley","license":[{"start":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T00:00:00Z","timestamp":1683849600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Gulf University for Science and Technology Seed Grant","award":["234271"],"award-info":[{"award-number":["234271"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2023,5,12]]},"abstract":"<jats:p>Developing new ways to estimate probabilities can be valuable for science, statistics, engineering, and other fields. By considering the information content of different output patterns, recent work invoking algorithmic information theory inspired arguments has shown that a priori probability predictions based on pattern complexities can be made in a broad class of input-output maps. These algorithmic probability predictions do not depend on a detailed knowledge of how output patterns were produced, or historical statistical data. Although quantitatively fairly accurate, a main weakness of these predictions is that they are given as an upper bound on the probability of a pattern, but many low complexity, low probability patterns occur, for which the upper bound has little predictive value. Here, we study this low complexity, low probability phenomenon by looking at example maps, namely a finite state transducer, natural time series data, RNA molecule structures, and polynomial curves. Some mechanisms causing low complexity, low probability behaviour are identified, and we argue this behaviour should be assumed as a default in the real-world algorithmic probability studies. Additionally, we examine some applications of algorithmic probability and discuss some implications of low complexity, low probability patterns for several research areas including simplicity in physics and biology, a priori probability predictions, Solomonoff induction and Occam\u2019s razor, machine learning, and password guessing.<\/jats:p>","DOI":"10.1155\/2023\/9696075","type":"journal-article","created":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T17:50:08Z","timestamp":1683913808000},"page":"1-15","source":"Crossref","is-referenced-by-count":4,"title":["Low Complexity, Low Probability Patterns and Consequences for Algorithmic Probability Applications"],"prefix":"10.1155","volume":"2023","author":[{"given":"Mohammad","family":"Alaskandarani","sequence":"first","affiliation":[{"name":"Centre for Applied Mathematics and Bioinformatics (CAMB), Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, Mubarak Al-Abdullah, Kuwait"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4423-3255","authenticated-orcid":true,"given":"Kamaludin","family":"Dingle","sequence":"additional","affiliation":[{"name":"Centre for Applied Mathematics and Bioinformatics (CAMB), Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, Mubarak Al-Abdullah, Kuwait"},{"name":"Department of Chemical Engineering and Biotechnology, Cambridge University, Cambridge, UK"},{"name":"Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA"}]}],"member":"311","reference":[{"issue":"639","key":"1","first-page":"376","article-title":"A preliminary report on a general theory of inductive inference (revision of report v-131)","volume":"49","author":"R. 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Alan","year":"1936","journal-title":"Journal of Mathematics"},{"key":"23","article-title":"Shannon information and kolmogorov complexity","author":"P. Grunwald","year":"2004"},{"key":"24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-0-387-84816-7_1","article-title":"Algorithmic probability: theory and applications","volume-title":"Information Theory And Statistical Learning","author":"R. J. Solomonoff","year":"2009"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1109\/tit.1976.1055501"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1186\/1748-7188-6-26"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1198\/016214501753168398"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/bti549"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2113883119"},{"key":"30","article-title":"Deep learning generalizes because the parameter-function map is biased towards simple functions","author":"G. 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